Here, a, b, and c are real numbers with a≠0. The term with the highest degree — the quadratic term — is written first. Then, the linear term followed by the constant term are written. The standard form can be used to determine the direction of the parabola, the y-intercept, the axis of symmetry, and the vertex.
|Direction of the Graph||Opens upward when a>0|
|Opens downward when a<0|
|Axis of Symmetry|
|Form||Equation||How to Rewrite?|
|Vertex Form||y=a(x−h)2+k||Expand (x−h)2, distribute a, and combine like terms.|
|Intercept Form||y=a(x−p)(x−q)||Multiply a(x−p)(x−q) and combine like terms.|